Cluster sizes in a classical Lennard-Jones chain

Abstract

The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, $⟨K⟩$, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that $⟨K⟩$ increases exponentially with $\beta =1/k_{B}T$ and with pressure, $P$ in agreement with previous results in the literature. A method is illustrated for using $⟨K⟩(\beta ,P)$ to generate a "phase diagram" for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.

Submitted to Phys. Rev. E. 5 figures

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